Quantizers based on various schemes have been proposed for efficiently encoding spectral coefficients in a frequency domain. For example, a quantizer based on trellis coded quantization (TCQ), uniform scalar quantization (USQ), factorial pulse coding (FPC), algebraic vector quantization (AVQ), and pyramid vector quantization (PVQ), etc. has been used. Accordingly, a lossless encoder optimized for each quantizer has been also implemented.